Question

The production manager of a clothing manufacturer estimates that the total annual cost of producing men’s suits is given by the equation: C = 5,000 + 4,100Q – 4.1Q2 + .004Q3. What is the minimum price the firm can accept to not shut down in the short run?

Answer 1

A minimum price the firm accept is the price equal to the minimum average variable cost.

The output at the level of minimum average variable cost is found by equating first differentiation equal to zero.

FC=the cost is same at all level and it is equal to total cost at Q=0

VC=TC-FC

VC=4,100Q – 4.1Q^2 + .004Q^3

AVC=VC/Q

AVC=4100-4.1Q+0.004Q^2

differentiation it and equating to zero

dAVC/dQ=-4.1+0.008Q=0

0.008Q=4.1

Q=512.5

AVC=4100-4.1Q+0.004Q^2

AVC=4100-4.1*512.5+0.004*512.5^2

AVC=3049.375=price

the firm will accept a minimum price of $3049.375